The existence of periodic solutions for coupled Rayleigh system

This paper is concerned with the existence of periodic solutions for coupled Rayleigh system (CRS). A sufficient criterion for the existence of periodic solutions for CRS is provided via an innovative method of combining graph theory with coincidence degree theory as well as Lyapunov method. As a subsequent result, coupled Lord Rayleigh system is also discussed. Subsequently, a sufficient condition is given to determine the existence of its periodic solutions. Finally, a numerical example and its simulations are presented to illustrate the effectiveness and feasibility of the proposed criterion.